The problem is to change their positions to those shown at the bottom
of the illustration in the shortest possible number of moves.

A move consists of placing the tips of the first and second fingers on
any two touching coins, always of the different sizes, then sliding
the pair to another spot along the imaginary line shown in the
illustration. The two coins in the pair must touch at all times. The
coin at left in the pair must remain at left; the coin at right must
remain at right. Gaps in the chain are allowed at the end of any move
except the final one. After the last move the coins need not
necessarily be at the same spot on the imaginary line that they
occupied at the start.